## Numerical Analysis for Applied ScienceNumerical Analysis for Applied Science is a graduate-level text suitable for both scientists and engineers as well as applied mathematicians. Each chapter begins with the motivation and construction of the methods under discussion moves on to practical considerations associated with their implementation, and concludes with an in-depth treatment of rigorous mathematical details. The chapter-end problem sets include both theoretical and computational exercises. |

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### Contents

Some Useful Tools | 1 |

Approximation of Functions | 27 |

Direct Methods for Linear Systems | 109 |

Band Matrices | 133 |

Errors and Iterative Improvement | 150 |

Solution of Nonlinear Equations | 161 |

Iterative Methods for Linear Systems | 221 |

Eigenvalue Problems | 283 |

Numerical Integration | 313 |

Ordinary Differential Equations | 349 |

Difference Methods for PDEs | 395 |

Introduction to Finite Elements | 447 |

Divided Differences | 477 |

Chebyshev Polynomials | 483 |

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### Common terms and phrases

algorithm analog apply associated basis functions bounded Chapter coefficients compute condition constant construct Corollary defined denote derivatives diagonal entries difference differentiable discuss eigenvalues eigenvectors Equation error estimate example Figure Fourier function f Gauss Gauss–Seidel graph grid function heat equation Householder transformations implies induction initial guess inner product inner-product space integral interpolant f interval a,b iterative scheme Jacobi method Lemma linear system Lipschitz LU factorization matrix norm mesh size h multistep scheme Newton-Cotes formulas Newton's method nodes nonsingular nonzero one-step method orthogonal permutation matrix pivoting polynomial interpolation positive definite problem PRoof prove QR decomposition quadrature row reduction satisfies secant method Section sequence ſº solve spline stepsize subinterval successive substitution symmetric and positive theorem triangle inequality tridiagonal truncation error upper triangular values vanishes vector space yields zero